The present invention relates to methods and apparatus for logging earth formations penetrated by a well borehole, and more particularly to methods for directly determining formation and borehole characteristics by analysis of gamma rays from naturally occurring formation radiation. This includes determining relative elemental abundancies of potassium (K), uranium (U), and thorium (Th), and measuring formation lighology in open holes and casing thickness in cased holes.
In recent years gamma ray spectroscopy of earth formations in the vicinity of a well borehole has been made practical by the development of highly stable scintillation detectors which may be lowered into a well borehole and which produce a pulse height spectrum proportional to the gamma ray energy spectrum of gamma ray impinging upon the scintillation crystal. In one commercially available well logging service for detecting the natural gamma ray spectra produced by uranium, potassium, and thorium in earth formations in the vicinity of a well borehole, three energy ranges or windows are used which are centered about selected gamma ray emission peaks for naturally occurring gamma rays in the decay chain of the aforementioned elements. Gamma ray count rates in each of these three energy ranges are transmitted to the surface and processed by a technique called spectrum stripping wherein standard calibration spectra for each of the individual elements (made in standard boreholes) are applied to the measurements of count rates made in the energy ranges chosen for detecting each of the three elements. So called "stripping constants" derived from the measurement of the standard spectra in standard boreholes for each of the three elements are then applied to the measured spectrum from the unknown earth formations surrounding the borehole. An estimate of the percentages of the particular three elements being measured is then made based on the stripping technique.
In a second, slightly more sophisticated commercially available technique, (such as that described in U.S. Pat. No. 3,976,878 to Chevalier, et al, issued Aug. 24, 1976) five energy ranges or windows are utilized for the measurement of the spectrum of natural gamma rays emitted by the earth formations in the vicinity of a well borehole. The five energy range measurements used in this technique are employed in a least squares fitting scheme to determine the elemental concentrations of the three elements, again based on the spectrum of each of the individual elements of the three taken in standard boreholes. The use of the five windows gives an overdetermined set of equations (i.e., 5 equations in 3 unknowns) which are statistically enhanced by the use of the count rate data from the extra two energy windows to distinguish this technique from that described in the foregoing paragraph.
A problem which occurs in the use of either of the above referenced prior art techniques is that the measurements of the gamma ray spectra of the unknown earth formations in each instance are compared with standard spectra for each of the individual elements made in standard borehole conditions. That is to say, standard condition borehole spectra are fitted to the spectra obtained in the unknown borehole being measured in each of the above two techniques. The problem arises due to the fact that the borehole conditions in the unknown earth formations being measured may not correspond to the conditions which existed in the standard, or calibration, spectra boreholes. That is to say, if the standard spectra were made with a scintillation detector placed in an eight inch borehole, the effect of the borehole dimensions of casing and mud conditions on unknown spectra taken in, for example, a six or twelve inch borehole could cause variations in the spectrum stripping or fitting techniques. These variations could affect the estimates of the percentage of the three elements sought to be detected by as much as an order of magnitude. The present invention takes into account the differences in borehole sizes, borehole effects, and borehole conditions from the standard gamma ray spectra used for the comparison to the unknown spectra taken in the borehole of interest.